The following line passes through point $(5, -2)$ : $y = -\dfrac{7}{12} x + b$ What is the value of the $y$ -intercept $b$ ?
Explanation: Substituting $(5, -2)$ into the equation gives: $-2 = -\dfrac{7}{12} \cdot 5 + b$ $-2 = -\dfrac{35}{12} + b$ $b = -2 + \dfrac{35}{12}$ $b = \dfrac{11}{12}$ Plugging in $\dfrac{11}{12}$ for $b$, we get $y = -\dfrac{7}{12} x + \dfrac{11}{12}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(5, -2)$